For more information you might want to read this paper. It states that the use of "Dativ-e" in common usage "bis zum 16. Jahrhundert im Oberdeutschen beinahe
vollständig, größtenteils im Westmitteldeutschen und partiell im Ostmitteldeutschen" came to a standstill. Furthermore, the use of "Dativ-e" in idioms is analyzed (2.2, some nice diagrams) and reasons are given why the usage in idioms is still common (rhyme, style, easier pronunciation, see paragraph 3).

Concerning your example the author researched that in the 20th century in the majority of cases (77,1%) the idiom was used with the "Dativ-e".